Marine biological resources are likely to come under increasing stress over the course of the 21st century as global climate change and ocean acidification interact with other stresses, including heavy fishing pressures and marine pollution, to create far reaching and difficult‐to‐predict changes in species abundance, spatial distribution, and trophic interactions. The governance systems in place for marine fisheries and for the marine environment, more broadly, will be critical in determining the extent to which these resources can be managed for sustainability. The paper focuses on the governance of internationally shared fisheries, and draws on a body of game‐theoretic research to discuss present‐day governance problems and to evaluate the implications of global environmental change for future efforts to maintain cooperative and effective governance of shared fishery resources. In particular, the increased likelihood of abrupt and unpredictable changes in the productive potential and migratory behavior of exploited fish stocks may threaten to disrupt cooperative management arrangements. The paper discusses the value of contingency planning based on anticipation of the possibility of such events and concludes with a discussion of future directions for both research and policy development.